Vindya Bhat, Jaroslav Nešetřil, Christian Reiher, Vojtěch Rödl
Published 2016-07-10Version 1
We construct a Ramsey class whose objects are Steiner systems. In contrast to the situation with general $r$-uniform hypergraphs, it turns out that simply putting linear orders on their sets of vertices is not enough for this purpose: one also has to strengthen the notion of subobjects used from "induced subsystems" to something we call "strongly induced subsystems". Moreover we study the Ramsey properties of other classes of Steiner systems obtained from this class by either forgetting the order or by working with the usual notion of subsystems. This leads to a perhaps surprising induced Ramsey theorem in which designs get coloured.
Graph-theoretic perspective on a special class of Steiner Systems
On the spectral radius of a class of non-odd-bipartite even uniform hypergraphs
Partitioning $2$-coloured complete $k$-uniform hypergraphs into monochromatic $\ell$-cycles
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